Our selection of study sites was based on the availability of historic hydrographic data that had sufficient point density and geospatial information to support meaningful comparisons with corresponding, more contemporary, lidar data. Each of our five study sites was analyzed independently over the specific time period indicated, using the oldest appropriate data available and the most recent data available. Our analysis was limited by the areal extent of available data sets. We note that there are gaps in the Florida Keys analysis where data were unavailable, including the Middle Florida Keys and near shore areas. There are also gaps in the Buck Island analysis in shallow areas surrounding the island and other areas where data were not collected. These gaps are identified in mapped results as white masked areas (Sect. 3.1). Full analysis of anthropogenic impact factors (e.g., urban extent, developed land, terrestrial water runoff, water quality) was beyond the scope of this study. However, our selected data sets spanned time periods during which human population approximately doubled and local anthropogenic impacts increased at each study site as well as at one uninhabited site (Table 2).

We caution that not all historical and modern data sets are appropriate for elevation-change analyses. Careful consideration must be given to the original purpose of the surveys, the horizontal and vertical resolution of paired historical and modern data sets for comparison, and the horizontal resolution of data relative to the total size of the study area. We specifically chose data sets that were collected for the purpose of uniform regional-scale mapping of seafloor depth/elevation without bias toward specific seafloor features (e.g., only shallow areas, manmade features) to minimize skewing of the data-point distribution. We performed multiple analyses to quantify and validate the horizontal and vertical error of the data sets (See Sect. 2.11, 2.12, 2.13), as well as the effect of horizontal resolution and alignment error on our results (See Sect. 2.13). Coarse horizontal resolution of many historical data sets limits their use for elevation-change analyses to only large, regional-scale areas such as those addressed in this study (Sect. 2.13).

We used historical hydrographic survey (H sheet) data collected by the United States Coast and Geodetic Survey (USC&GS) or the National Ocean Service (NOS) between 1934 and 1982. These historical data included digital XYZ sounding data for water depth as well the accompanying descriptive reports and smooth sheets (final map renderings) and were downloaded from the National Oceanic and Atmospheric Administration's (NOAA) Office of Coast Survey. The number of H sheets used for each study site varied from 1 to 24 depending on geographic area. All data sources and descriptions are listed in Table 3. During these surveys several methods were used to collect depth soundings by USC&GS/NOS including lead line, graduated sounding pole, and fathometer, and the methodology was noted in each H sheet descriptive report along with measurement resolution information.

In general, for the 1930s surveys, sounding poles were often used in water depths approximately less than 3 m and replaced with lead lines at greater depths. Sounding positions for 1930s data were determined by sextant triangulations using both permanent and temporary topographic reference points or triangulation stations, theodolite fixes, navigational beacons, and ship time and speed fixes (Shalowitz, 1964). Most of the surveys after 1960 were performed using a fathometer and augmented with lead line soundings. The historical sounding data for Buck Island and Maui, collected using a fathometer, were reported to the nearest tenth of a fathom (0.18 m) for water depths less than 20 fathoms (37 m) and 11 fathoms (20 m), respectively, and to the nearest 1 fathom (1.8 m) for greater water depths. Therefore, we only used data from shallower depths than these thresholds (0.18 m resolution) at these study sites. Following field surveys, hydrographic data went through quality control protocols including adjustment for tides, removal of erroneous points, validation of track line cross soundings, and determination of agreement with adjacent surveys to create a published smooth sheet (Shalowitz, 1964). The descriptive reports include notes from the USC&GS/NOS survey teams and details on any adjustments or changes made by reviewers. Hydrographic data used in our study that were downloaded from NOAA Office of Coast Survey had already been digitized by personnel at NOAA.

The US Office of Coast Survey imparted strict standards on collection of historical hydrographic data from the 1800s to the 1950s that allowed for less error than later, in the 1900s, when electronic means of collecting sounding data replaced lead lining and poling (Shalowitz, 1964). For data collected by the Coast Survey from the late 1800s to 1950s, maximum allowable vertical differences at crossing data points were 0.06 m for depths less than 4.6 m and 0.46 m for depths between 22 and 29 m (Byrnes et al., 2002). Lead line and poling vertical resolution reported for the historical data sets that we used was 0.15 m (similar to that of lidar), while fathometer resolution was 0.3 m. Furthermore, sounding poles were used in depths less than 3 m (where many shallow patch reefs are located). Many H sheet descriptive reports indicated that the water was clear enough during surveys to see the bottom (which improves accuracy of the measurement). The most common error likely to occur during use of lead lines or sounding poles was overestimation of water depth due to angling of the line or pole as currents move the boat past the point of measurement. Overestimation of historical water depth would erroneously decrease elevation losses calculated using our methods. Therefore, it is more likely that our erosion estimates are underestimated rather than overestimated due to lead line and poling techniques. We estimated horizontal error for historical data sets of approximately 5.0 m (See Sect. 2.13).

Lidar data sets from the USGS Coastal and Marine Geology lidar program and the US Army Corps of Engineers (USACE) Joint Airborne Lidar Bathymetry Technical Center of Expertise (JALBTCX) were downloaded for each study site (Table 3, US Army Corps of Engineers-JALBTCX, 1999, 2004; Brock et al., 2006a, 2007; Fredericks et al., 2015a, b). Lidar-derived DEMs for Atlantic/Caribbean and Pacific sites were at horizontal spatial resolutions of 1 and 4 m, respectively, with horizontal datums of UTM NAD83 and vertical datums of NAVD88 GEOID03 for the Atlantic, VIVD09 for the Caribbean, and MLLW for the Pacific. Vertical accuracy of lidar data is typically reported as the 95 % root-mean-square error (RMSE) (Hodgson and Bresnahan, 2004). Vertical RMSEs for the lidar data used in this study ranged from 0.135 to 0.15 m as reported in the metadata accompanying the lidar data for each site and based on independent validation by in-water acoustic-based depth measurements at the time of collection.

We performed visual inspection of all of the historical (H sheet) data relative to 2016 aerial and satellite imagery with a resolution of 1 m (2016 World Imagery from ArcGIS online via ArcMap 10.2.2; sources: Esri, DigitalGlobe, GeoEye, Earthstar Geographics, CNES/Airbus DS, USDA, USGS, AEX, Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community) to measure differences between stable coastal and geographic features following the methods of Lukas (2014) for use of historical elevation data sets. Visual inspection of map features that have not changed over the study period allows for confirmation of general horizontal alignment of the compared data sets. For example, in the Upper Florida Keys a historic bridge was surveyed in the 1930s and still existed at the time this study was performed. We overlaid the georectified 1934 H sheet on 2016 georectified WorldView imagery in ArcMap 10.2.2 and used software-measuring tools to examine the offsets in this structure. The maximum offset of bridge boundaries between historical and modern locations was 4.8 m (Fig. 2). This offset is similar to the sum of errors reported in our horizontal error analysis in Sect. 2.13. We were able to identify other stable, rocky coastlines and/or manmade features (such as shoreline berms) for these types of comparisons at all study sites. In offshore areas, we examined locations in the historical data where the boundaries of large patch reefs were outlined by soundings when depths were too shallow for a boat to pass over the reef, causing deviations from linear transect lines. There were no significant misalignments between historical and modern boundaries for reefs that experienced minimal erosion. We performed these visual inspections for all historical (H sheet) data from all study sites and found similar alignment agreement. Additionally, we visited select areas at all study sites to visually inspect the seafloor for erosion or accretion features that were consistent with trends identified by our analysis.

The historical sounding data were corrected for sea level rise that occurred from the time of its collection to the time of collection of the corresponding lidar data. We adjusted the historical soundings using NOAA relative sea level rise (RSLR) estimates to account for any differences at local tide stations caused by sea level rise, platform movement, and/or subsidence (Parker, 1992; Byrnes et al., 2013). Long-term sea level rise data (in millimeter per year) recorded by NOAA sea level trend stations near our study sites were used to calculate the total sea level rise at each study site by multiplying the mean rate of annual sea level rise over the study time period (mm yr-1) by the number of years between historical and modern data sets. These correction values ranged from approximately 7 to 16 cm and were added to the historical sounding value. NOAA reports 95 % confidence intervals for these data ranging from approximately ±0.15 to ±0.81 mm yr-1. The potential error from these corrections was insignificant relative to other sources of error, and we, therefore, excluded it from our RMSE calculations. Sea level trend stations, rates, and correction factors are presented in Table 4.

Vertical units for the original historical sounding measurements were converted from feet and fathoms to meters by the NOAA Office of Coast Survey but remained in their original vertical datum (reference surface of zero elevation). We determined vertical datums for the digitized soundings by reviewing the H sheet descriptive reports and smooth sheet notes. Historical sounding data were reported relative to tidal datums of mean low water (MLW) or mean lower low water (MLLW). Comparison between historical and modern data sets required transferring sounding data to the same vertical datum as the corresponding lidar data so elevations could be compared relative to a common zero elevation system. NOAA also transferred horizontal datums (coordinate systems for identifying physical locations) of the digitized XYZ historical hydrographic data to North American Datum 1983 (NAD83) during the digitization process. Similarly, historical data required transformation to the same horizontal datum as corresponding lidar data. We performed these data transformations using publicly available software from NOAA called VDatum v3.6 (available along with user guides and tutorials at https://vdatum.noaa.gov/). Geospatial and transformation information for these conversions is provided in Table 4, and a more detailed description of the transformation procedure is provided in Supplement 1.1.

The horizontal spacing of the historical sounding points was much coarser than the resolution of the lidar DEMs (1 to 4 m). Average historical sounding point densities for each whole study site were 109, 89, 422, 268, and 326 pts km-2 for the UFK, LFK, STT, BI, and Maui, respectively. Therefore, we used the locations of the historical soundings to extract modern elevation values from the lidar DEMs. This approach is more accurate than creating an interpolated model surface (or DEM) from the historical data and then determining elevation change from two interpolated surfaces. Digital data files containing the XYZ coordinates for historical elevations were used with spatial analyst tools in ArcMap 10.2.2 to extract lidar elevation values at the XY locations of historical soundings to create a single data file that contained the X and Y coordinates and the corresponding historical and lidar elevation values (see Supplement 1.2 for processing steps).

The data files created during the extraction process in Sect. 2.5 were used to calculate elevation changes (Zchange) by subtracting the historical elevation data from the corresponding modern elevation data via Eq. (1). Zchange=modern  lidar  elevation  data  point-historical  elevation  data  point Using this equation, negative values indicate loss of seafloor elevation and positive values indicate gain of seafloor elevation. The resulting data files for each study site are located in Tables S1, S2, S3, S4, and S5 in the Supplement and are also available in Yates et al. (2017). These files contain data columns for the historical H sheet source, year of historical data value, latitude and longitude in geographic and UTM coordinates, historical elevation values (m), modern lidar elevation values (m), and the difference in meters (Zchange) between historical and modern elevations, as well as vertical and horizontal datum information (see Supplement 1.3 for processing steps). These data sets were used for elevation-change analysis of each study site including calculation of mean elevation change and analysis of elevation change by habitat type. We note that much reef degradation contributing to elevation change likely occurred after 1970 (Gardner et al., 2003; Bruno and Selig, 2007; Jackson et al, 2014). Therefore, data sets containing pre-1970s data (Table 3) could be biased toward lower annual elevation and volume-change rates.

We used the XYZchange (northing, easting, and Zchange) data sets created in Sect. 2.5 for elevation analysis of each study site and of each habitat type within each study site. Mean elevation change and standard deviation were calculated for the total area of each study site using all Zchange data points. We used benthic habitat maps for the Upper and Lower Florida Keys from the Florida Fish and Wildlife Conservation Commission (2015) and for the USVI and Maui from NOAA (Kendall, 2001a, b; Battista and Christensen, 2007) to delineate the boundaries of all habitat classes within each site. We calculated elevation-change statistics from the data points included within or on the boundary of each habitat including maximum elevation losses and gains, total number of elevation-loss data points, mean elevation loss and standard deviation, total number of elevation-gain data points, mean elevation gain, and standard deviation. We also calculated elevation-change statistics for combined habitat classes within each study site that included only coral-dominated substrate (e.g., scattered coral rock in unconsolidated sediment, aggregate reef, reef rubble, individual or aggregate patch reefs, spur and groove), as well as for combined habitat classes that included only adjacent habitats (e.g., non-coral-dominated substrate types such as sand, seagrass, macroalgae, pavement, unconsolidated sediment). Coral-dominated substrate types within each study site that were combined for these calculations were denoted with an asterisk and adjacent habitats were indicated by the absence of an asterisk in data tables. We created an ArcMap “model” to automate the XYZchange data-point processing for calculation of elevation-change statistics to ensure consistency for each habitat class (see Supplement 1.4 for data processing steps).

We created a single elevation-change surface model for each study site to estimate seafloor volume change, using the XYZchange data points calculated in Sect. 2.5. We used the Delaunay triangulation algorithm (in ArcGIS 10.2.2) to create a triangulated irregular network (TIN) from these data points. The TIN consists of a comprehensive, three-dimensional network of triangles spanning the entire data set. The three-dimensional location of the vertices of each triangle was determined by using the XY data to establish its horizontal position and the Zchange data to establish its vertical position in the network of triangles. TIN modeling allows for placement of nodes over irregular surfaces, allowing for higher resolution over surface areas that are highly variable (such as coral reefs). Delaunay triangulation creates the triangle network such that no vertex lies within the interior of any of the circumcircles of the triangles in the network to avoid creation of long, thin triangles that can degrade surface resolution (http://pro.arcgis.com/en/pro-app/help/data/tin/tin-in-arcgis-pro.htm). Figure 3 shows examples of (a) the XYZchange data plot, (b) the three-dimensional TIN model developed from the XYZchange data, (c) a subsection of the TIN model, and (d) a horizontal cross-section view of the TIN model subsection for the Upper Florida Keys study site. In Fig. 3b, c, and d, the zero elevation-change plane lies between positive elevation-change values (denoted in blue tones) and negative elevation-change values (denoted in red tones). The gray areas in Fig. 3b and c and the dashed lines in Fig. 3d indicate all elevation-change values between +0.5 and -0.5 m (90 % RMSE). See Supplement 1.5 for data processing steps.

We calculated volume changes (in units of millions of cubic meters, 106 m3) for each study site using the surface models created in Sect. 2.8. Maximum volume-change calculations included all elevation-change data. Minimum volume-change calculations excluded all elevation-change data within or equal to plus or minus 0.5 m (see Fig. 3 for Upper Florida Keys example). The 0.5 m threshold was derived from our vertical error analysis (see Sect. 2.11). We calculated volume change for four cases based on placement of a reference plane within the surface model as follows:

gross accretion (maximum volume), in which plane height is set to 0.0 m and volume is calculated above the plane;

We used the benthic habitat maps referenced in Sect. 2.7 (also used for elevation-change calculations) to delineate habitat boundaries for calculation of volume changes for each habitat class within each study site. Habitat classes within each map were represented by individual polygons. We created new TIN models for each habitat polygon that only covered the areal extent of the specific habitat class polygon where it intersected the whole study site TIN. We calculated minimum and maximum volume changes for gross erosion and gross accretion in each habitat class using the four reference plane cases described in Sect. 2.9. We calculated volume changes for combined habitat classes within each study site including combined coral-dominated substrate and combined adjacent habitat using the same habitat combinations and procedures similar to those used for combined habitat elevation-change statistics described in Sect. 2.7 and using processing steps in Supplement 1.7.

US federal standards were applied for all vertical and horizontal data transformations and error analyses. Our vertical error analysis included error terms for

RMSESounding, the uncertainty for each historical data set as determined from our analysis of repeat measurements that were performed by the original surveyors at the time of data collection;

These uncertainty values (RMSE values) are specific to each data set and are reported in Table 5.

We determined RMSESounding for each historical data set from repeat sounding measurements collected by the original surveyors. When historical sounding data were collected, repeat surveys were performed along select transect lines and/or additional soundings were collected along intersecting transects for the purpose of determining vertical accuracy. Only maximum difference of repeat data points was reported as accuracy information in the historical data set descriptive reports. We, therefore, reanalyzed all of the historical repeat and cross-track line survey data from the original historical data sets to perform a more rigorous, systematic vertical-error analysis (rather than simply using the reported maximum difference). We calculated the mean difference in depth between all pairs of repeat measurements within each historical data set and used these data to calculate an RMSESounding for each data set using Eq. (2) whereby di,1 and di,2 were paired repeat depth measurements and n was the number of sounding-point pairs used for each location (see Supplement 1.8 for procedures to identify repeat sounding measurements). RMSESounding=∑i=1ndi,1-di,22n

The number of sounding-point pairs used for each location was 40, 253, 40, and 51 for the UFK, STT, STC, and Maui, respectively. The LFK was excluded from this analysis because no adjacent points were separated by 5 m or less. Implicit in this approach is the assumption that the points in each pairing represent two independent depth measurements at approximately the same location. Therefore, the mean difference in depth between all pairs should not be significantly different from 0 m. For each study site, we performed a two-tailed t test at the α=0.05 level on the set of depth differences between paired points to test the null hypothesis of a zero mean difference. t tests were performed using Matlab v8.4.0 (R2014b). All of the RMSESounding values ranged from 13 to 32 cm and are reported in Table 5 along with t tests results.

The maximum cumulative uncertainty (MCU) reported by NOAA National Ocean Service (2016) for operational VDatum regions of South Florida and the Virgin Islands are 9.6 cm and 11.8 cm respectively. Our calculated RMSEVDatum for the UFK, LFK, STT and BI study sites fell within reported MCU values (Table 5). No vertical transformations were performed for the Maui data because both historical and modern elevation data were collected and reported relative to MLLW; therefore, RMSEVDatum was excluded from vertical error estimates for this study site.

We followed the general approach used by the US Army Corps of Engineers (Byrnes et al., 2002) to calculate composite RMSE (RMSETotal) for each study site (Table 5) according to Eq. (3) to provide conservative estimates of elevation changes based on combined sources of uncertainty. RMSETotal=RMSESounding2+RMSElidar2+RMSEVDatum2 Our average RMSETotal (Table 5) for all study sites was 0.29 m and ranged from 0.20 to 0.37 m. Our average RMSETotal (0.29 m) was similar to that reported for lidar and acoustic sounding data and half the reported value for previous studies that used nautical chart data to create a DEM for examining the response of a reef to sea level rise (Leon et al., 2013; Hamylton et al., 2014). We then calculated a more conservative RMSETotal for each study site. We considered the RMSETotal values from each study as proxies for the standard deviations. Data within plus or minus 1 standard deviation of the mean encompasses approximately 68 % of the variability in a normal distribution; data within plus or minus 2 standard deviations of the mean encompass approximately 95 % of the variability. We used the normal inverse cumulative distribution function to calculate that 90 % of our elevation-change values would occur within plus or minus 1.65 standard deviation of the mean. We then multiplied the RMSETotal values by 1.65 (denoted 1.65 × RMSETotal) to capture approximately 90 % of the variability in the depth differences. The average 1.65 × RMSETotal for all study sites was 0.48 m, which we rounded to 0.5 m and applied to all of our study sites for calculation of minimum volume changes.

Within our study sites, the most stable areas were likely those classified as pavement or bedrock. We performed an analysis of these habitat types to independently estimate the potential vertical error associated with comparing historical and modern sounding data. We caution that this type of analysis does not constitute a true control because no subaqueous surface areas (including stable pavement or bedrock) are exempt from elevation change. For example, our data indicated areas where pavement had been exposed likely due to erosion of overlying sediments, as well as areas where pavement had been buried likely by deposition of sediments, growth of corals, etc. However, areas were identified in each data set where little to no elevation change was also observed. We examined habitats labeled “pavement” in the UFK and LFK, “uncolonized pavement” in STT, “colonized pavement” in BI, and “coral pavement” in Maui. We filtered the elevation-change data points for these habitats to include only elevation changes of less than ±0.5 m (1.65 × RMSETotal). We then calculated the average difference and standard deviation between these points for each data set.

More than 50 % of elevation-change points for pavement in the UFK, STT, and BI, 17 % in the LFK, and 23 % in Maui showed elevation changes within our 1.65 × RMSETotal of 0.5 m. Standard deviations for these locations were all within our RMSETotal of 0.29 m. Mean differences between historical and modern elevation data in these locations were very small (ranging from 3 to 6 cm; Table 6), indicating that vertical resolution and accuracy of historical and modern elevation data are comparable. Large standard deviations relative to the means and histograms showing skewed distribution of data points from this analysis (Fig. 4) demonstrate that all areas of pavement are not stable and, therefore, should not be considered a true control.

No horizontal error was reported for any historical data sets. Our historical sounding data sets ranged from the 1930s to 1980s. Therefore, we determined the potential horizontal error associated with our oldest data sets from the 1930s in the Florida Keys as an estimate of maximum horizontal error for all study sites. The Florida Keys historical soundings were measured using the least accurate horizontal positioning methods and had average point densities that were more than 50 % lower than the other study sites.

The original horizontal datum for data sets from the Florida Keys was North American Datum 1927 (NAD27). Transformation of data from NAD27 to NAD83 using NOAA National Ocean Service program NADCON introduces no more that 15 cm of uncertainty in the continental United States (Dewhurst, 1990). The Annual Report of the US Coast and Geodetic Survey 192 (1880) indicates that it was possible under normal controls to measure distances (using triangulation) with an accuracy of 1 m, and the position of the plane table could be determined within 2 to 3 m of its true position (Shalowitz, 1964). The horizontal resolution of lidar data is reported as better than 1m (Brock et al., 2006a, b, 2007; Fredericks et al., 2015a, b). A sum of these estimated sources of error is approximately 5 m. We chose to sum these estimated sources of error to provide a more conservative error estimate rather than to calculate a horizontal RMSE. This error estimate is similar to the maximum offset of 4.8 m between the historical and modern measurements of a bridge structure located south of Lower Matecumbe Key in the UFK as depicted on a 1934 H sheet and on the 2016 World Imagery identified during visual inspection of H sheets described in Sect. 2.2.

Horizontal error of approximately 10 m is typically reported for data plotted at a 1:20000 scale (Anders and Byrnes, 1991; Fletcher et al., 2003; Morton et al., 2004). Therefore, we performed a horizontal shift analysis to test the potential impact for systematic plus random horizontal error of up to 10 m that represents an approximate doubling of our sum of estimated sources of error (5.0 m). Historical XYZ elevation data from the Upper and Lower Florida Keys were shifted by 10 m to the north, south, east, and west by adding 10 m to, and subtracting 10 m from, UTM northings and eastings for each data point (26 341 and 1688 points for the Upper and Lower Florida Keys, respectively). This exercise generated four new, experimental historical XYZ elevation point data sets that simulate up to 10 m of horizontal error in each of four directions. The area of the unshifted lidar DEMs for each site was clipped to each of the four shifted historical data sets generated for each study site, resulting in four new pairs of historical and modern elevation data sets for each study site. Elevations from the lidar DEMs were then extracted at each historical point location for each paired historical and modern data set and used to calculate elevation differences between the shifted historical soundings and unshifted lidar data sets as described in Sect. 2.6. We created new TIN models from the shifted XYZchange point data sets and calculated volume changes for each of these data sets using the TIN modeling process and surface volume analysis described in Sect. 2.8 and 2.9.

Results from the horizontal shift analysis indicate that 10 m of horizontal error produces no more than 10 % difference in net and area-normalized volume change calculations in the Upper Florida Keys and up to a 21 % difference in the Lower Florida Keys (Table 7) likely due to the lower density of data points over a smaller geographic area. The LFK had the lowest historical sounding point density of all data sets at 89 pts km-2 and the smallest study site area of 19 km2. Imparting 10 m of horizontal error in these experimental data sets does not change the general conclusion of our study indicating high magnitude of net erosion at these study sites. Our results are consistent with reports that over large areas (such as in our study), random errors largely cancel out relative to change calculations derived from two surfaces (Byrnes et al., 2002).

Loss of seafloor elevation and volume, as well as transition from net accretion to net erosion, has occurred at all study sites (Table 8). Mean seafloor elevation losses for whole coral reef ecosystems in our study ranged from -0.09 to -0.8 m. Note that mean elevation changes (“mean elevation-change” columns in Tables 8 and 9) represent the net change encompassing all negative (elevation losses) and positive (elevation gains) values. Figures 5, 6, and 7 show the complex spatial distribution and large range of elevation gains and losses across the study sites. Individual measurements of elevation-change were often very large (greater than 1 m; see minimum and maximum elevation loss and gain data by habitat in Table 9). Maximum elevation losses exceeded 4.0 m and maximum elevation gains exceeded 6.5 m at all study sites. Therefore, standard deviations for mean elevation changes were high and ranged from 0.7 to 1.5 m for all sites.

Net volume losses were also observed in all regions indicating export of sediments from these systems (Table 8). Minimum volume changes (calculated by excluding elevation-change data within a vertical range of ±0.5 m, see 1.65 × RMSE calculations in Table 5) provide conservative estimates of net volume losses ranging from 0.2 × 106 to 52.8 × 106 m3 for all study sites. Maximum volume changes (including all elevation-change data) indicate net volume losses ranging from 3.4 × 106 to 80.5 × 106 m3 for all study sites.

We analyzed 118 710 elevation-change data points from 60 habitats across all five study sites. Fifty-nine of these habitats showed net elevation change, 46 (77 %) showed net elevation losses, and 13 (22 %) showed net elevation gains (Table 9). The “mean loss” column in Table 9 (that includes only elevation-loss values within habitats) indicates that only two habitats showed mean losses less than our RMSETotal of 0.29 m (STT reef rubble and BI seagrass). Only 14 habitats showed mean losses less than our 1.65 × RMSETotal of 0. 5 m (that encompasses 90 % of the variability). Therefore, mean losses in 97 % of the habitats we analyzed were greater than our vertical RMSETotal of 0.29 m, and 77 % of the habitats we analyzed showed mean losses greater than 1.65 × RMSETotal or 0.5 m. In several cases, and particularly associated with coral-dominated substrate, mean losses exceeded 1 m. Conversely, if one examines only elevation-gain values within habitats (“mean gain” column in Table 9), mean gains in 92 % of the habitats were greater than our RMSETotal of 0.29 m and 60 % showed mean gains greater than our 1.65 × RMSETotal of 0.5 m.

Greatest mean elevation losses were generally associated with shallow, coral-dominated habitats (Tables 8 and 9) at all study sites consistent with observations of general flattening of reef topography (Alvarez-Filip et al., 2009) and observations of decreasing abundance of reef-building corals (Gardner et al., 2003; Bruno and Selig, 2007; Jackson et al., 2014; Sparks et al., 2015). However, greatest net volume losses at most study sites were generally associated with adjacent (non-coral-dominated) habitats despite smaller mean elevation losses. This apparent contradiction is due to the greater areal extent of these habitats (Tables 8 and 10). Maximum values of area-normalized volume change calculated using all elevation-change data (Table 8) indicate that volume loss in adjacent habitats was 40 to 100 % of losses observed in coral-dominated substrate. We calculated the percent of each study site classified as coral-dominated substrate to estimate the potential contribution of loss of framework-building coral species to total net volume loss (coral-dominated habitat classes were denoted in Tables 9 and 10 with an asterisk). For example, the Upper Florida Keys coral-dominated habitat classes included scattered coral rock in unconsolidated sediment, aggregate reef, reef rubble, individual or aggregate patch reefs, and spur and groove habitat. The other study sites included similar lists of coral-dominated habitats. We included reef rubble as a coral-dominated substrate in our calculations because, for example, in the Florida Keys many areas of reef rubble contain large skeletal fragments of Acropora palmata and other coral species, and we note that framework-building coral species such as Acropora sp. declined significantly throughout the Caribbean and western Atlantic during the time periods of our study (Jackson et al, 2014). Areal extent of coral-dominated substrate was only 8 to 15 % of the total study area in the UFK, LFK, and STT study sites and contributed up to only 26 % of the total net volume loss. Most of the volume loss in these areas was associated with sediment loss from non-coral-dominated (adjacent) habitats such as areas of unconsolidated sediments, seagrass, and uncolonized pavement. Areal extent of coral-dominated substrate was higher at the Maui study site (57 %) and contributed more than 50 % to net volume loss; adjacent habitats accounted for the remaining volume loss. The considerable loss of seafloor volume in adjacent habitats at these study sites and in coral-dominated habitats, as well as large total net volume losses, suggests that physical erosion and export of sediments is a likely driver of much of the volume loss we observed.

The BI study site had the highest areal extent of coral-dominated substrate (91 %) that contributed more than 90 % to the total net volume loss, suggesting that degradation of framework-building corals may be the primary contributor to volume loss at this study site. Recent photographic surveys (C. Storlazzi, USGS, 2015) along the eastern coast of Buck Island show large stands of Acropora palmata coral colonies that have died and toppled over, but they remain largely in tact and in place on the seafloor along the northeastern side of the island from approximately the eastern-most point to at least the mid-point of the island (Fig. 8a, b, and c), consistent with our observation of greater elevation loss in that area (Fig. 6c). The southeastern side of the island, from the eastern-most point to at least the barrier break, was characterized by much more live A. palmata coral (Fig. 8d, e, and f), also consistent with our observation of increased elevation in that area (Fig. 6c). These photos illustrate how loss of topographic complexity (as described by Alvarez-Fillip et al., 2009) can cause elevation and volume loss without material export. The live coral colonies clearly show relatively high elevation and colony volume that consists of both coral branches as well as very large open (pore) spaces between the branches. As large colonies topple, the coral branches break and the colony compacts, causing a loss in elevation and volume as the open spaces between the branches are minimized. Large coral fragments are much harder to transport than sediments, typically require high-energy storm events for movement, and are, thus, not as easily exported from the system. Additionally, coral rubble fields generated from toppling corals can create a rubble pavement on top of sand making it more difficult to transport. Mean elevation and volume losses were much lower at the BI study site than at the other study sites, indicating that much less sediment was exported from the system, consistent with our observations of large areas of physically toppled coral colonies that remain mostly in place on the seafloor. This type of physical coral degradation is very different from degradation of reef structure due to bioerosion by reef grazers such as parrotfish and Diadema sp. sea urchins, which directly reduce coral and reef structure to sand-sized sediments that can then be more easily transported and exported by physical processes, and from chemical bioerosion caused by some species of sponges and endolithic algae that dissolve carbonate material (Decarlo et al., 2015; Enochs et al., 2015; Reyes-Nivia et al., 2013; Wisshak et al., 2012, 2013; Tribollet et al., 2009). As population abundances of bioeroders increase and decrease in a given location, so do rates of bioerosion caused by these organisms (Mumby, 2009). Populations of grazing bioeroders have decreased at the BI study site and throughout most of the Caribbean during the time periods of our study (Table 1) that may account for the lower export rates at this study site because coral and coral rubble may be reduced to sand at a slower rate. Visual inspection of study sites in the Florida Keys shows similar evidence for physical toppling of corals in rubble fields. However, parrotfish populations recently increased in the Florida Keys (Table 1) and rates of chemical bioerosion have increased since preindustrial times (Enochs et al., 2015), which may help expedite breakdown and physical transport of reef materials out of the system, consistent with the higher volume losses observed in the Florida Keys.

Along the Florida Keys reef tract within Biscayne National Park, Florida, and the Florida Keys National Marine Sanctuary, mean elevation and volume losses occurred in 9 of 11 habitat classes in the UFK reef tract (Fig. 5a, b) and in 6 of 9 classes in the LFK reef tract (Fig. 5c, d), including coral habitats and adjacent habitats such as unconsolidated sediments, pavement previously covered by sediments or coral, and seagrass. Largest mean elevation losses occurred at shallow patch and aggregate reefs, and coral-dominated and reef rubble habitats, consistent with documented declines in abundance of large framework-building corals over the past several decades (Jackson et al., 2014). Largest net volume losses occurred in seagrass and unconsolidated sediment habitats. Mean elevation and volume gains occurred in deep water habitats of the UFK and LFK sites, including offshore aggregate reefs in the LFK near a sanctuary preserve area, at the base of spur-and-groove habitat along fore-reef slopes, and where relic spur-and-groove formations in-filled with sediments indicating transport of reef sediments down the fore-reef slope and export offshore (Fig. 9). Mean total elevation loss was lowest at the UFK study site. However, mean elevation losses decreased from upper (-0.4 m) to central (-0.3 m) subregions of the UFK, and mean elevation increased slightly in the lower subregion (0.1 m) primarily associated with seagrass habitat (Fig. 5a, b). Notably, the lower subregion is further away from high-density population areas north of the study site and near an area of the middle Florida Keys identified as a possible refuge from ocean acidification due to seagrass productivity (Manzello et al., 2012). The LFK site included the Looe Key National Marine Sanctuary and Special Protection Area (Fig. 5c). Net elevation and volume losses were similar to the central subregion of the UFK possibly due to close proximity to high-density population areas in the Lower Florida Keys. However, the LFK was the only study site that showed net accretion in combined coral habitat classes. Accretion is partially attributed to deep reef and spur-and-groove habitat that has been buried by sand (Lidz et al., 2007). Redistribution of reef materials and erosion of the Florida reef tract is corroborated by field observations of movement and deposition of meters-thick sand deposits likely due to hurricanes and by exposure of older reef material from erosion and transport (Shinn et al., 2003). However, accretion was also observed on offshore aggregate reef habitat near the Special Protection Area.

Mean elevation and volume loss occurred in 16 of 17 habitat classes in STT (Fig. 6a, b). In STT, small, localized areas of coral-dominated substrate showed gains in elevation. However, greatest mean elevation losses occurred in coral-dominated habitats and near the central coastline where harbor and shipping channels exist. Mean elevation and volume gains only occurred on uncolonized bedrock possibly due to transport and deposition of sediments. However, uninhabited Buck Island National Reef Monument and Marine Park, St. Croix USVI (BI), showed less mean elevation and volume loss than all other sites with losses limited to 4 of 11 habitat classes including 3 coral habitats (Fig. 6c, d). The study period for BI is approximately 10 years shorter than for nearby STT. Greatest mean elevation gains in BI occurred along linear reef near the shoreline. Most elevation and volume gains occurred within Buck Island National Reef Monument and Marine Park boundaries (Fig. 6c), suggesting that distance from populated areas combined with managed protection has limited losses at this site.

Mean elevation and volume loss occurred in 10 of 12 classes in Maui (Fig. 7a, b). Mean elevation and area-normalized volume losses were at least 2 to 3 times greater, respectively, than all other study sites and occurred over a shorter time frame. These greater losses may be caused by higher sediment export rates due to a combination of higher wave energy, physical erosion, and a narrow shallow shelf surrounding the island allowing sediment to be more easily transported offshore into deep water, as has been observed in other high-energy reef environments (Morgan and Kench, 2014; Perry et al., 2015). Greatest mean elevation losses were associated with coral-dominated habitat as well as “not classified” habitat located in the bank/shelf zone that may be impacted by slumping of materials along steeply sloping areas. Elevation and volume gains occurred in mud and rubble habitats and may be associated with terrigenous sediment transport from the island.

Examination of histograms for pavement analysis data supports the general observations for each of our study sites. Histograms for the UFK, LFK, STT, and Maui (Fig. 4a, b, c, e) are all skewed toward negative values, consistent with regional-scale trends of seafloor elevation loss and export of sediments at these sites. While BI (Fig. 4d) showed a more even distribution of points among elevation losses and gains consistent with the lower regional-scale mean elevation losses observed at this study site and suggestive of redistribution and less export of sediments within the system. Notably, of the five study sites we examined, the “colonized pavement” in BI was the only pavement habitat to show a very small increase in elevation that could be due to either coral growth on the pavement or accumulation of sediments.